While Monolith Soft isn't ready to announce anything yet, the company has shared interest in creating some games that spawn from original IP. This news comes from an interview with Yasuyuki Honne and Tomohiro Hagiwara. With recent projects, Monolith Soft has been working on Nintendo-owned IP. They hope to let the Kyoto studio strut their stuff with an original creation sometime in the future.

That nintendosoup article is wrong.
The ''original IP'' quote was about hoping their Kyoto Studio can work on new
games parallel to what the Tokyo studio does in the future, rather than the support
role they have now.
Nothing to do with the state of their IPs or future ones, as they'll always belong to Nintendo too.

Technically, it is possible for the studio to self-publish something and release it on their own, but it’d have to be Switch-exclusive. Rare did the same thing back in the N64 days with Banjo, Perfect Dark and Killer Instinct.

Actually NEVERUNPLAYING, unlike the situation with Rare, anything Monolith Soft makes would still belong to Nintendo. Its not really "self publishing" when you ARE Nintendo as well (as Monolith Soft is a 1st party studio).

Rare was never owned by Nintendo, so they could freely self publish as well as getting to keep their own creations that were not part of Nintendo's IP (or its universe). Nintendo was only able to have Rare keep those games on Nintendo consoles as Nintendo did own a good chunk of Rare (just not the controlling share).

Rare was never fully owned by Nintendo though, they were just a second party affiliate like Hal, among others. Monolith Soft is subsidiary of Nintendo. Nintendo fully owns them, so could they really self publish without Nintendo's permission?

Nintendo owns a majority of Monolithsift (80%), with Namco and the studio’s higher ups owning the rest. They’ve developed games since the buyout without Nintendo’s involvement too (Project X Zone, DBZ: Attack of the Saiyans, Super Robot Taisen OG - all Namco published). The possibility is there, it just requires them to 100% fund it, which would be tough and perhaps not worth it. I believe Brownie Brown and Creatures did smaller games like that too.

This means, from Monolith Soft's own site, that Nintendo owns 96.66% of Monolith Soft.

With Project X Zone 1 & 2, Nintendo was the one allowing Monolith Soft to do this game with Namco, as Nintendo & Namco are close. Even Project X Zone 2 was using 3 Nintendo owned characters (Which Monolith Soft would NOT be able to use without Nintendo's permission. Chrom & Lucina from Fire Emblem, Fiora from Xenoblade Chronicles)

Creatures is not owned by Nintendo, and own 1/3 of the Pokemon franchise just like GameFreak & Nintendo (though unlike Creatures & GameFreak, Nintendo has sole trademark rights giving them the ultimate Veto Power over all things Pokemon).